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Simora [160]
4 years ago
12

Identify the zeros of the function f(x) = 2x^2 − 4x + 5 using the Quadratic Formula

Mathematics
1 answer:
Nostrana [21]4 years ago
3 0

For this case we have that by definition, the roots, or also called zeros, of the quadratic function are those values of x for which the expression is 0.

Then, we must find the roots of:

2x ^ 2-4x + 5 = 0

Where:

a = 2\\b = -4\\c = 5

We have to:x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}

Substituting we have:

x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (5)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-40}} {4}\\x = \frac {4 \pm \sqrt {-24}} {4}

By definition we have to:

i ^ 2 = -1

So:

x = \frac {4 \pm \sqrt {24i ^ 2}} {4}\\x = \frac {4 \pm i \sqrt {24}} {4}\\x = \frac {4 \pm i \sqrt {2 ^ 2 * 6}} {4}\\x = \frac {4 \pm 2i \sqrt {6}} {4}\\x = \frac {2 \pm i \sqrt {6}} {2}

Thus, we have two roots:

x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}

Answer:

x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}

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A total of 937 people attend the play. Admission was $2.00 for adults and $0.75 for students. The totral ticket sales amounted t
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Answer:

x = students

y = adults

Linear Systems of Equations :

x + y = 937

0.75x + 2y = 1,109

Step-by-step explanation:

Step 1 : eliminate one of the variables

x + y = 937

0.75x + 2y = 1,109

-2(x + y = 937) = -2x - 2y = -1874

-2x - 2y = -1874

0.75x + 2y = 1109

We can eliminate y since -2y + 2y = 0

Step 2: Find x number of students.

-2x = -1874

+0.75x = 1109

____________

-1.25x = -765

____________ = 612 students attended

     -1.25

937 - 612 = 325 adults

Check Answer :

612 x 0.75 = $459

325 x 2 = $650

$650 + $459 = $1,109

Therefore, there will be 612 students attending and 325 adults.

6 0
3 years ago
Find the value of the expression (-101)+102+(-103)+104+...+(-199)+200. (with steps)
Juliette [100K]
 hello : 
<span>(-101)+102+(-103)+104+...+(-199)+200
=(  </span>(-101)+(-103) +....+ (-199) ) +( (102) + ( 104) +....+(200))
let : A = (  (-101)+(-103) +....+ (-199) )
       B = ( (102) + ( 104) +....+(200))
note : the sum n term of arithemtic sequence 
S= n/2(u1 + un)
 un = u1 +(n-1) d       u1 : the first term      d : the common diference
in A :  u1= -101      d = -2       n = 49... 
in B : u1 =102       d=2        n= 49
A = 49/2(-101-199) =-7350
B=49/2(102+200)=4949
(-101)+102+(-103)+104+...+(-199)+200 = A+B =-2401
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
(10 points) From a group of 9 men and 7 women a committee consisting of 4 men and 4 women is to be formed. How many different co
alexgriva [62]

Answer:

a) 2450

b) 1890

c) 1050

Step-by-step explanation:

Given:

- Available Group = 9 M & 7 F

- Committee of= 4 M and 4 W to be formed

Find:

- (a) 2 of the men refuse to serve together?

- (a) 2 of the women refuse to serve together?

- (a) 1 man and 1 woman refuse to serve together?

Solution:

- The question pertains to a selection process, We will use combinations for each case as follows.

part a)

- Since 2 men cant be selected together. Then we have to discount for one man while selecting Man for the committee. Hence, the combinations are:

                                   8C4 x 7C4 = 2450

part b)

- Since 2 women cant be selected together. Then we have to discount for one woman while selecting them for the committee. Hence, the combinations are:

                                   9C4 x 6C4 = 1890

part b)

- Since 1 women and a man cant be selected together. Then we have to discount for one woman and one man while selecting them for the committee. Hence, the combinations are:

                                   8C4 x 6C4 = 1050

4 0
4 years ago
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